Math Question

Question

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Let $r$ be the positive real solution to $x^3 + \frac{2}{5} x - 1 = 0.$ Find the exact numerical value of $r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb.$

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NewMember Jan 5, 2020

edited by NewMember Jan 5, 2020

Guest · Answer 1 · 2020-01-05T06:16:52

From the formula for a geometric series, the sum is 19/3.

heureka · Answer 2 · 2020-01-06T10:10:28

Let $r$ be the positive real solution to $x^3 + \dfrac{2}{5} x - 1 = 0$ .
Find the exact numerical value of $r^2 + 2r^5 + 3r^8 + 4r^{11} + \dotsb$ .